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\begin{document}

The stop events of this regime will occur where $\rho$ jumps from $0$
to $1$, which means $\sigma Q-\lambda g+P_e$ will equal to zero at
$T_4$.

As long as $k_B$ is positive, we could also prove that $j$ is positive
until the technology progress $\mu_B$ reaches its upper limit $\bar{H}$.
\begin{Prop}
\label{Prop:jpos}
If renewable energy capital $k_B>0$ and the technology progress
$\mu_B<\bar{H}$, then investment in renewable energy efficiency $j$ is
also positive.
\end{Prop}
\proof Suppose $j=0$ when $k_B>0$ and $\mu_B<\bar{H}$. From \eqref{eq:FOCj},
we have $\omega\ge0$ and $\omega_H=\lambda-(1-\psi)\eta k_B^\psi
j^{-\psi}$. When $j=0$, the latter expression of $\omega_H$ is negative, which is contradicted
to $\omega\ge0$. Hence, $j$ has to be positive when $k_B>0$ and
$\mu_B<\bar{H}$.
\endproof
\subsection{Regime 5: Renewable energy improvements through learning by doing}

The analysis in the previous section can be extended to the previous
regime where both energy efficiency of end-use capital and the
efficiency of renewable energy production are increasing. As the limit on the efficiency of renewable energy production looms, the incentive to invest in renewable R\&D will disappear since $h$ will continue to rise as a result of learning by doing even when $j=0$.

The only differences relative to regime 6 are that the energy market equilibrium condition changes to
\begin{equation}
(F_0-af)k=(H_0+bh)k_B
\label{eq:Reg7EnEquil}
\end{equation}
while $h$ evolves according to $\dot{h}=k_B$ and the corresponding co-state variable $\eta$ is no longer equal to zero. We thus obtain a new co-state equation:
\begin{equation}
\dot{\eta}=\beta\eta-p_ebk_B
\label{eq:Reg7etadot}
\end{equation}
Also, the remaining co-state equation (apart from \eqref{eq:iiFPos}) that is analogous to \eqref{eq:Reg7Costate} becomes
\begin{equation}
\dot{\lambda}=(\beta+\delta)\lambda-\eta+\lambda m-p_e(H_0+bh)
\label{eq:Reg7Costate}
\end{equation}
Paralleling the analysis in the previous section, \eqref{eq:Reg7Costate} can be combined with \eqref{eq:iiFPos} and expression \eqref{eq:Enprice} for $p_e$ to again yield a relationship between capital stocks that has to hold along the balanced growth path
\begin{equation}
(F_0-af)\biggl [\lambda(\delta+m)-\eta\biggr ]+ak\biggl [\lambda(A+m)-\eta\biggr ]=\lambda(A-\delta)(H_0+bh)
\label{eq:Reg7fkrel}
\end{equation}
Once again, we can differentiate \eqref{eq:Reg7fkrel} to obtain a relationship between the investments $i_F, i_B$ and $i$ that need to hold to maintain the balanced growth path. In doing this, we use \eqref{eq:Enprice} to eliminate $p_e$ from \eqref{eq:Reg7etadot} and note that $\dot{h}=k_B$. Specifically, differentiating \eqref{eq:Reg7fkrel} results in a relationship between $i$ and $i_F$ that can be simplified to
\begin{equation}
\biggl [\lambda(A+m)-\eta\biggr ]i-\biggl [\lambda(\delta+m)-\eta\biggr ]i_F=\biggl \{(A-\delta)\eta+\delta\bigl [\lambda(A+m)-\eta\bigr ]\biggr\}k
\label{eq:j0iiFrel}
\end{equation}
A second relationship  between the investments can be obtained by differentiating the energy market equilibrium condition \eqref{eq:Reg7EnEquil}, which leads to:
\begin{equation}
(F_0-af)i-aki_F-(H_0+bh)i_B=bk_B^2
\label{eq:j0iiBiFrel}
\end{equation}
Equations  \eqref{eq:j0iiFrel} and \eqref{eq:j0iiBiFrel} can then be solved for $i_F$ and $i_B$ in terms of $i$. Substituting the results, along with the solution for $c$, into the budget constraint, we can then determine $i$ and thence $i_F$ and $i_B$.

The upper boundary of this regime will occur where $h=(\bar{H}-H_0)/b$. We again require $k, \lambda$ and $f$ to be continuous across that boundary. To obtain the ``initial condition'' for the shadow price $\eta$, we use the transversality condition at $T_7$. Specifically, the value of $T_7$ is itself a choice variable since different initial value of $\eta$ will lead to different levels of investment in $h$ and hence different times at which $h$ attains its maximum value. Hence, the marginal effect of a change in $T_7$, namely the current value of the Hamiltonian at $T_7$ plus $\partial V/\partial t$, must equal zero.  But  $\partial V/\partial t$ is given by:
\begin{equation}
\frac{\partial}{\partial T_7}\biggl [\int_{T_7}^\infty e^{-\beta(\tau-T_7)}\frac{c(\tau)^{1-\gamma}}{1-\gamma} \,d\tau\biggr ]=-\frac{c(T_7)^{1-\gamma}}{1-\gamma}
\label{eq:MargTermValue}
\end{equation}
where $c$ is the optimal consumption path. The current value Hamiltonian will be given by \eqref{eq:Hamiltonian} evaluated at $T_7$. The budget constraint \eqref{eq:Budget} and the energy market equilibrium \eqref{eq:EnEquil} will both hold with equality. In this regime $j, \rho, n, i_R , q_R$ and $\sigma$ are all zero  while $q_B=\lambda=\varphi$. Hence, the Hamiltonian at $T_7$ will equal
\begin{equation}
\begin{split}
\frac{c(T_7)^{1-\gamma}}{1-\gamma}+\lambda (i-\delta k+i_B-\delta k_B+i_F)+\eta k_B
\end{split}
\label{eq:HamT6}
\end{equation}
Thus, the transversality condition at $T_7$ will require
\begin{equation}
\eta(T_7)k_B=-\lambda(i-\delta k+i_B-\delta k_B+i_F)<0
\label{eq:etaT6}
\end{equation}
Since learning by doing continues to increase $h$ beyond $T_6$, when explicit investment in $h$ ceases to be worthwhile, it is not surprising that the terminal value of its shadow price $\partial V/\partial h$ should be negative at $T_7$. From the first order condition \eqref{eq:FOCj} for $j$, throughout the preceding regime 6 we will have $\lambda>\eta \psi k_B$ so the lower boundary of regime 7 will occur where $\eta\psi k_B=\lambda>0$.

\subsection{Calibration}

In order to quantitatively evaluate different policy scenarios, we first need to calibrate the theoretical model. This involves assigning numerical values to certain parameters in a way that make the model consistent with observations from the actual world economy. By definition, we start the economy with $S=N=H=k_B=0$ and with $Q=Q_{0}$. For convenience, we take the current population $Q_{0}=1$ and effectively measure future population as multiples of the current level. We will assume that the population growth rate is 1\%.\footnote{This is consistent with a simple extrapolation of recent world growth rates reported by the Food And Agriculture Organization of the United Nations, \textsf{http://faostat.fao.org/site/550/default.aspx}}

In line with standard assumptions made to calibrate growth models, we assume a time discount factor $\beta =0.05$. From previous analyses of macroeconomic and financial data, we would expect the coefficient of relative risk aversion $\gamma$ to lie between 1 and 10, but there is no strong consensus on what the value should be. As we explain in more detail below, we will allow $\gamma$ to adjust to ensure we match the initial share of consumption in GDP.

To calibrate values for the initial production, capital stocks and energy quantities we used data from the \textit{Energy Information Administration} (EIA),\footnote{International data is available at \textsf{http://www.eia.doe.gov/emeu/international/contents.html}} the \textit{Survey of Energy Resources 2007} produced by the \textit{World Energy Council},\footnote{This is available at \textsf{http://www.worldenergy.org/publications/survey\_of\_energy\_resources\_2007/default.asp} The data are estimates as of the end of 2005.} and \textit{The GTAP 7 Data Base} produced by the \textit{Center for Global Trade Analysis} in the Department of Agricultural Economics, Purdue University.\footnote{Information on this can be found at \textsf{https://www.gtap.agecon.purdue.edu/databases/v7/default.asp} The GTAP 7 data base pertains to data for 2004.} The last mentioned data source is useful for our purposes because it provides a consistent set of international accounts that also take account of energy flows.

One of the first issues we need to address is that national accounts include government spending in GDP, which does not appear in the model.\footnote{Note that in the GTAP data base, aggregate world exports equal aggregate world imports so world GDP equals consumption plus investment plus government expenditure.} We therefore subtracted government spending from the GDP measures before calibrating the remaining variables. Conceptually, this would be correct if the utility obtained from government spending were additively separable from the utility obtained from private consumption and government spending was financed by lump sum taxes. In practice, neither of these assumptions is valid and government activity (apart from energy taxes or subsidies, which will be considered explicitly later) would affect the equilibrium of the model.

After excluding government, the investment share of private sector expenditure is 0.2569. Effectively defining units so that aggregate output is 1, we therefore identify 0.2569 as the sum $i+i_F+i_R+n$ at $t=0$. We would expect most of this to be investment in capital used to produce final output rather than end-use energy efficiency improvements or improvements in fossil fuel mining and conversion activities.

Converting the GTAP data base estimates of the total capital stock capital stock to units of GDP, we obtain the initial condition $k(0)+k_R(0)=3.2802$. The GTAP data does not allocate the capital stock to different sectors, but it does give new capital purchases by sector. Identifying mining of coal, oil, and natural gas, refining, electricity production from coal, oil and natural gas, and gas distribution as the fossil fuel mining and conversion sectors, we obtain that 6.91\%, or 0.2267 of the capital would be $k_R(0)$ while $k(0)=3.0535$.

Given that we have chosen units so the $R=1$, this also implies that the energy efficiency parameter $\epsilon=1/k_R(0)=0.2772$. Similarly, if we choose GDP units so that output equals 1, the parameter $A$ would equal the ratio of output to capital, that is, $A$ also is 0.2772. We also use the GTAP depreciation rate on capital of 4\%.

From the budget constraint, the difference between total output and the sum of the investments, namely 0.7431 would equal consumption plus the current costs $gR$ of supplying fossil fuels. We separated these two components using sectoral data from the GTAP data base. Specifically, we classified ``energy expenditure'' as combined spending on the primary fuels coal, oil and natural gas, and the energy commodity transformation sectors of refining, electricity generation and natural gas distribution. In effect, we are associating $gR$ with the costs involved in mining fossil fuels and turning them into commodities capable of providing energy services to productive capital. The current cost of fossil energy was then set equal to the expenditure on these sectors that was classified as consumption rather than investment. This produced a value for $gR=0.0565$. Observe that, assuming $R=1$, this value of $g$ implies fossil fuels yield positive net output at $t=0$, that is, $A-\delta-g/\epsilon=0.0335>0$ but an increase of $g$ to just 0.0658 would erase this marginal surplus.

Subtracting the initial value for $gR$ from 0.7431 we obtain the initial value of $c(0)=0.6867$. As noted above, the normal method of solving the optimal control problem would involve specifying values for the parameters and the state variables and then solving for values of the co-state variables that allow us to hit required terminal values. The value for $c(0)$ would then follow from the first order condition $\lambda(0)=c(0)^{-\gamma}$. To obtain a particular value for $c(0)$ we need to free up an additional parameter. As already noted above, we will introduce $c(0)$ as a new target and adjust the value of $\gamma$ as $\lambda(0)$ changes to ensure that  $\lambda(0)=c(0)^{-\gamma}$ always remains valid.

After we set the initial values of $S$ and $N$ to zero, the initial value for $gR$ also would imply
\begin{equation}
\frac{0.0565}{R}=\alpha _{0}+\frac{\alpha _{1}}{\bar{S}-\alpha _{2}/\alpha_{3}}
\label{eq:Init_g}
\end{equation}
We can choose energy units so that the initial value of $R=1$ by definition. However, we still need to know the worldwide annual production of fossil fuels in order to calibrate other energy terms in the same units. The EIA web site gives world wide production of oil in 2005 of 175.896 quads (where one quad equals $10^{15}$ BTU), of natural gas 100.141 quads and of coal 123.03 quads. Summing these gives a total of 392.637 quads, which we will take as our measure of one unit of ``energy services''.

To obtain an estimate of total fossil fuel resources $\bar{S}$ in the same units, we used data from the World Energy Council and the US Geological Survey (USGS). The millions of tonnes of coal, millions of barrels of oil, extra heavy oil, natural bitumen and oil shale and trillions of cubic feet of conventional and unconventional natural gas were converted to quads using conversion factors available at the EIA. The result is 21.780 quintillion BTU of coal, 20.369 quintillion BTU of conventional and unconventional oil and . These resources are nevertheless relatively small compared to estimates of the volume of methane hydrates that may be available. Although experiments have been conducted to test methods of exploiting methane hydrates, a commercially viable process is yet to be demonstrated. Partly as a result, resource estimates vary widely. According to the National Energy Technology Laboratory (NETL),\footnote{\textsf{http://www.netl.doe.gov/technologies/oil-gas/FutureSupply/MethaneHydrates/about-hydrates/estimates.htm}} the United States Geological Survey (USGS) has estimated potential resources of about 200,000 trillion cubic feet in the United States alone. According to Timothy Collett of the USGS,\footnote{\textsf{http://www.netl.doe.gov/kmd/cds/disk10/collett.pdf}} current estimates of the worldwide resource in place are about 700,000 trillion cubic feet of methane. Using the latter figure, this would be equivalent to 719.6 quintillion BTU. Adding this to the previous total of oil, natural gas and coal resources yields a value for $\bar{S}=834.8$ quintillion BTU or around 2126.1769 in terms of the energy units defined so that $R=1$.

We still need to specify values for the $\alpha_i$ parameters in the $g$ function. Equation \eqref{eq:Init_g} with $R\equiv 1$ will give us one equation in four unknowns. Noting that we can interpret $\bar{S}-\alpha_2/\alpha_3$ as the initial level of fossil fuel extraction $S$ at which marginal costs of extraction $g(S,0)$ would become unbounded, we associate  $\bar{S}-\alpha_2/\alpha_3$ with current proved and connected reserves of fossil fuel.\footnote{Note that current official reserves are not the relevant measure since many of these are not connected and thus are unavailable for production without further investment, denoted $n$ in the model.} A recent report from Cambridge Energy Research Associates (CERA, 2009),\footnote{``The Future of Global Oil Supply: Understanding the Building Blocks,'' Special Report by Peter Jackson, Senior Director, IHS Cambridge Energy Research Associates, Cambridge, MA.} for example, gives weighted average decline rates for oil production from existing fields of around 4.5\% per year. They also note that this figure is dominated by a small number of ``giant'' fields and that, ``the average decline rate for fields that were actually in the decline phase was 7.5\%, but this number falls to 6.1\% when the numbers are production weighted.'' As an approximation, we shall use 6\% as a decline rate for oil fields. Using United States natural gas production and reserve figures as a guide, we find that natural gas decline rates are closer to 8\% per year. The United States data coal mine decline rates approximate 6\% per year. In accordance with these figures, we assume the ratio of fossil fuel production to proved and connected reserves equals the share weighted average of these figures, namely $(175.948\ast 0.06+100.141\ast 0.08+116.6\ast 0.06)/392.689=0.0651$. Thus, in terms of the energy units defined so that $R=1$, the initial target value of $\bar{S} -\alpha_2/\alpha_3$ would equal 1/0.0651=15.361. Using the previously calculated value for $\bar{S}$, this leads to $\alpha_2/\alpha_3=2110.538$.

We can obtain two more equations by examining the investment in fossil fuel production at $t=0$. Using GTAP data on capital shares by sector, we estimate that around 8.4\% of annual investment occurs in the oil, natural gas, coal, refining, electricity, and gas distribution sectors. We noted above that in the GTAP data, total investment $i+n=0.2569$, implying that $n\approx 0.0215$ in private sector output units. We assume that this level of investment at $t=0$ is sufficient to replace mined resources and allow for growth in total annual fossil fuel production equivalent to the average annual growth over 2004-08 of around 2.35\%.\footnote{These calculations are again based on data from the EIA.} Specifically, with $\alpha_2/\alpha_3=2110.538$, we assume that the investment $n=0.0215$ increases reserves by the amount mined $R=1$ plus 2.35\% of 15.361, that is, $\alpha_2/(\alpha_3+0.0215)=2109.195$, which implies $\alpha_3\approx 33.261$. The previously calculated value for $\alpha_2/\alpha_3$ then implies $\alpha_2 \approx 70198.52$. Next, we observe that the partial derivatives of $g$ depend on $\alpha_1, \alpha_2$ and $\alpha_3$ but not on $\alpha_0$. Using the previously calculated values for $c(0)$ and $k_R(0)$ and the guessed values for $\lambda(0)$ and $\sigma(0)$ we choose $\alpha_1$ so that equation \eqref{eq:nReg1} solves for $n=0.0215$. Specifically, using the expressions \eqref{eq:PartialgPartialN}, \eqref{eq:Partial2gPartialN2} and \eqref{eq:Partial2gPartialSN} for the partial derivatives of $g$, \eqref{eq:nReg1} becomes a linear equation in $\alpha_1$:
\begin{equation}
\begin{split}
\frac{\alpha_1\alpha_2}{(\bar{S}\alpha_3-\alpha_2)^2}&\biggl [2n(0)\biggl (\frac{k_R(0)\bar{S}}{\bar{S}\alpha_3-\alpha_2}+1\biggr )+k_R(0)\biggl (\delta-A+\frac{\sigma(0)}{\lambda(0)\epsilon}+\frac{g(0)}{\epsilon}\biggr )+c(0)-\frac{2\alpha_3k_R(0)^2}{\epsilon(\bar{S}\alpha_3-\alpha_2)}\biggr ]
\\ & =-\frac{\sigma(0)\pi}{\lambda(0)}
\end{split}
\label{eq:alpha1eqn}
\end{equation}
Finally, using the calibrated value of 0.0565 for $g$ we can then solve for $\alpha_0=g-\alpha_1/(\bar{S}-\alpha_2/\alpha_3)$.

Turning next to the learning curve \eqref{eq:RenewCost}, the literature
provides a range of estimates for $\alpha $. An online calculator provided
by NASA\footnote{Available at \textsf{http://cost.jsc.nasa.gov/learn.html}} gives a range of
learning percentages between 5 and 20\% depending on the industry. A
learning percentage of $x$, which corresponds to a value of $\alpha
=-ln(1-x)/ln(2)$, has the interpretation that a doubling of the experience
measure will lead to a cost reduction of $x$\%. Thus, $x=0.2$ is equivalent
to $\alpha =0.322$ while $x=.05$ corresponds to $\alpha =0.074$. In a study
of wind turbines, Coulomb and Neuhoff (2006)\footnote{Louis Coulomb and Karsten Neuhoff, \textquotedblleft Learning Curves and
Changing Product Attributes: the Case of Wind Turbines\textquotedblright ,
University of Cambridge: Electricity Policy Research Group, Working Paper
EPRG0601.} found values of $\alpha $ of 0.158 and 0.197. In a 1998 paper, Gr\"{u}bler and Messner\footnote{Arnulf Gr\"{u}bler and Sabine Messner, \textquotedblleft Technological
change and the timing of mitigation measures\textquotedblright , \textit{Energy Economics} 20, 1998, 495--512} found a value for $\alpha =.36$ using
data on solar panels. In a 2008 paper in \textit{The Energy Journal}, van
Bentham et. al.\footnote{\textquotedblleft Learning-by-doing and the optimal solar policy in
California,\textquotedblright\ Arthur van Benthem, Kenneth Gillingham and
James Sweeney, 29(3) 2008, 131-152} report several studies finding a
learning percentage of around 20\% ($\alpha =0.322$) for solar panels. For
our base case, we will take $\alpha =0.25$.

The other parameter affecting the incentive to invest in renewable energy sources is the initial value $\Gamma _{1}^{-\alpha }$ of the cost of renewable energy capital relative to fossil fuel capital. Using a document available from the Energy Information Administration (EIA) \footnote{\textit{Assumptions to the Annual Energy Outlook, 2010} available at \textsf{http://www.eia.doe.gov/oiaf/aeo/electricity\underline{ }generation.html}} the levelized capital cost of new onshore wind capacity is about six times the cost of combined cycle gas turbines (CCGT), while offshore wind is around seven times as expensive, solar thermal about ten times as expensive and solar photovoltaic more than seventeen times as expensive. On the other hand, geothermal and biomass capacity is only about four times as expensive, and nuclear and hydro about five times as expensive as CCGT. As a rough approximation, we will assume that the initial value of $\mu=\Gamma _{1}^{-\alpha }$ is around 5. We also assume that, in the long run, the renewable technologies can experience a five-fold reduction in costs, so their long run capital cost would be about 20\% above the current capital cost of fossil fuel technologies.

To fix the O\&M cost for renewables, $m$, we note that the same EIA document gives a fixed O\&M cost of onshore
wind that is around one-fifth the corresponding fixed plus variable (including fuel cost) O\&M for CCGT. The corresponding ratio is around one-half for offshore wind, one-tenth for solar photovoltaic, around one-half for nuclear and geothermal and one-fifth for hydro. As an approximation, we assume that $m$ equals 0.2 times the initial value of $g$, that is, 0.0113. Observe that for these values of $m,\delta, \Gamma_1$ and the previously set value for $A$, $A\Gamma_1^\alpha-\delta-m=0.0042>0$ as we assumed.

Finally, we need to specify a value for $\psi $, the relative effectivenessof direct investment in research versus learning by doing in accumulatingknowledge about new energy technologies. Klaassen et. al. (2005)\footnote{Klaassen, Ger, Asami Miketa, Katarina Larsen and Thomas Sundqvist,\textquotedblleft The impact of R\&D on innovation for wind energy inDenmark, Germany and the United Kingdom,\textquotedblright\ \textit{Ecological Economics}, 54 (2005) 227--240} estimated a model that allowedfor both learning-by-doing and direct R\&D. Although they assume the capitalcost is multiplicative in total R\&D and cumulative capacity, while we assume the \textit{change} in knowledge is multiplicative in new R\&D and cumulativecapacity, we can take their parameter estimates as a guide. They find directR\&D is roughly twice as productive for reducing costs as islearning-by-doing.\footnote{Of course, the learning-by-doing has the advantage that it directlycontributes to output at the same time it is adding to knowledge.} Consequently, we assume that $\psi =2$.

\newpage

\begin{thebibliography}{99}
\bibitem{} Aghion P., N. Bloom, R. Blundell, R. Griffith, and P. Howitt
(2002): Competition and Innovation: An Inverted U Relationship. \textit{NBER}
Working Paper

\bibitem{} Aghion P., and P. Howitt (1992): A Model of Growth Through
Creative Destruction. \textit{Econometrica} 60

\bibitem{} Apollo-Alliance (2004): The Apollo Jobs Report: Good Jobs and
Energy Independence, New Energy for America. \textit{The Apollo Alliance}

\bibitem{} Arrow K.J. (1962): \textquotedblleft The Economic Implications of
Learning by Doing,\textquotedblright\ \textit{American Economic Review}

\bibitem{} \textit{European Commission: Directorate-General for Research}
(2005): Energy R\&D Statistics in the European Research Area EUR 21453

\bibitem{} Chakravorty U., Roumasset J., and K. Tse (1997): Endogenous
Substitution among Energy Resources and Global Warming,\textquotedblright\
\textit{Journal of Political Economy} 105(6)

\bibitem{} Gaffigan M.E. (2008): Advanced Energy technologies. Testimony
Before the Subcommittee on Energy and Environment, Committee on Science and
Technology, \textit{House of Representatives}

\bibitem{} Hartley P. and K. Medlock III (2005): Carbon Dioxide: A Limit to
Growth? Manuscript

\bibitem{} Heal G. (1976): \textquotedblleft The Relationship Between Price
and Extraction Cost for a Resource with a Backstop
Technology,\textquotedblright\ \textit{Bell Journal of Economics}, The
\textit{RAND} Corporation, vol. 7(2), p. 371-378

\bibitem{} International Energy Agency (2000): Experience Curves for Energy
Technology Policy, OECD

\bibitem{} Kammen D.M. and G.F. Nemet (2005): Real Numbers: Reversing the
incredible shrinking US energy R\&D budget. \textit{Issues in Science and
Technology} 22(1), 84-88

\bibitem{} Klette T.J. and S. Kortum, \textquotedblleft Innovating Firms and
Aggregate Innovation,\textquotedblright\ \textit{Journal of Political Economy%
}, 204, 968-1018

\bibitem{} Kouvaritakis, N., Soria, A. and Isoard, S. (2000): Modelling
energy technology dynamics: methodology for adaptive expectations models
with learning by doing and learning by searching. \textit{International
Journal of Global Energy Issues} 14, 104--115

\bibitem{} Kydland, F. and E.C. Prescott, (1982) \textquotedblleft Time to
Build and Aggregate Fluctuations,\textquotedblright\ \textit{Econometrica}

\bibitem{} Margolis R.M. and D.M Kammen (1999): Evidence of under-investment
in energy R\&D in the United States and the impact of federal policy.
\textit{Energy Policy} 27, 575-584

\bibitem{} Nemet G.F. and D.M. Kammen (2007): \textquotedblleft U.S. energy
research and development: Declining investment, increasing need, and the
feasibility of expansion,\textquotedblright\ \textit{Energy Policy} 35

\bibitem{} Oren S.S. and S.G. Powell (1985): \textquotedblleft Optimal
supply of a depletable resource with a backstop technology: Heal's theorem
revisited,\textquotedblright\ \textit{Operations Research}, 33(2), 277--292

\bibitem{} Pollin R., Garrett-Peltier H.m Heintz, J., and H. Scharber
(2008): \textquotedblleft Green Recovery: A Program to Create Good Jobs and
Start Building a Low-Carbon Economy.\textquotedblright\ \textit{The Center
for American Progress} and \textit{Political Economy Research Institute},
University of Massachusetts, Amherst

\bibitem{} Popp D. (2002): Induced Innovation and Energy Prices, \textit{%
American Economic Review}, 32

\bibitem{} Solow R.M. and F.Y. Wan (1976): \textquotedblleft Extraction
Costs in the Theory of Exhaustible Resources,\textquotedblright\ \textit{%
Bell Journal of Economics}, The \textit{RAND} Corporation, vol. 7(2), p.
359-370,

\bibitem{} Wolfe R.M. (2004): Research and Development in Industry. \textit{%
National Science Foundation}

\bibitem{} United States Department of Energy

\bibitem{} United States Patent Office

\bibitem{} Universidad Rey Juan Carlos (2009): \textit{Study of the effects
on employment of public Aid to Renewable Energy Sources. }Research Director:
Gabriel Calzada Alvarez
\end{thebibliography}
